Lactose-free dairy. A group of researchers studying lactose-free dairy products report in their study that these products can provide the essential nutrients present in regular dairy products, like calcium and vitamins, to those that cannot digest lactose in nutrients (Vol. 11, 2019). The report also states that an average of 10 vegans have suffered bone fractures within two years after reaching the age of 60 due to the lack of calcium.

a. Construct arguments both for and against the use of the Poisson distribution to characterize the number of vegans who have suffered bone fractures within two years after the age of 60.

b. For the remainder of this exercise, assume the Poisson distribution is an adequate approximation for x, the number of vegans who have suffered bone fractures within two years after the age of 60. Find E1x2 and the standard deviation of x.

c. Based strictly on your answers to part

b, is it likely that more than 25 vegans aged 60 will suffer bone fractures in the next two years? Explain.

d. Find P1x 7 252. Is this probability consistent with your answer to part c? Explain.